{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Moving Obstacles\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Moving_Obstacles.ipynb)\n",
    "\n",
    "This example shows how to add moving obstacles to a fluid simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define our domain size and the obstacle behavior.\n",
    "A cube and sphere should move with constant velocity through the domain.\n",
    "Each step, the obstacle positions are incremented by $v \\cdot \\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = Box(x=100, y=100)\n",
    "obstacles = [\n",
    "    Obstacle(Cuboid(vec(x=20, y=80), x=20, y=20), velocity=vec(x=5., y=0)),\n",
    "    Obstacle(Sphere(x=20, y=20, radius=10), velocity=vec(x=1, y=4)),\n",
    "]\n",
    "\n",
    "def move_obstacle(obs: Obstacle, dt):\n",
    "    x = (obs.geometry.center + obs.velocity * dt) % domain.size\n",
    "    return obs.at(x)\n",
    "\n",
    "move_obstacles = lambda *obstacles, dt: tuple([move_obstacle(o, dt) for o in obstacles])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's sketch out the path the obstacles are going to take. We stack snapshots at different times along the `time` dimension which we make *spatial* in order to draw the snapshots with connecting lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "obs_trj = iterate(move_obstacles, spatial(time=6), *obstacles, dt=6.)\n",
    "plot([o.geometry for o in obs_trj], alpha=.5, overlay='list')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the simulation and run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(v, p, obs1, obs2, dt=.5):\n",
    "    obs1, obs2 = move_obstacles(obs1, obs2, dt=dt)\n",
    "    v = advect.mac_cormack(v, v, dt)\n",
    "    v, p = fluid.make_incompressible(v, (obs1, obs2), Solve(x0=p))\n",
    "    return v, p, obs1, obs2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1965dd5f06844b1283af5e45d2dbfd58",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/130 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v0 = StaggeredGrid(0, PERIODIC, domain, x=100, y=100)\n",
    "v_trj, p_trj, *obs_trjs = iterate(step, batch(time=130), v0, None, *obstacles, range=trange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"864\" height=\"360\" controls autoplay loop>\n",
       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAIGZ0eXBNNFYgAAACAE00ViBpc29taXNvMmF2YzEAAAAIZnJlZQADr1ltZGF0AAACrwYF//+r\n",
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1fd180cd8b0>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(*[o.geometry for o in obs_trjs], v_trj.curl(), animate='time', overlay='args')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "name": "python",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
